Transient Climate Response in a Two-Layer Energy-Balance Model. Part II: Representation of the Efficacy of Deep-Ocean Heat Uptake and Validation for CMIP5 AOGCMs

In this second part of a series of two articles analyzing the global thermal properties of atmosphere-ocean coupled general circulation models (AOGCMs) within the framework of a two-layer energy-balance model (EBM), the role of the efficacy of deep-ocean heat uptake is investigated. Taking into account such an efficacy factor is shown to amount to representing the effect of deep-ocean heat uptake on the local strength of the radiative feedback in the transient regime. It involves an additional term in the formulation of the radiative imbalance at the top of the atmosphere (TOA), which explains the nonlinearity between radiative imbalance and the mean surface temperature observed in some AOGCMs. An analytical solution of this system is given and this simple linear EBM is calibrated for the set of 16 AOGCMs of phase 5 of the Coupled Model Intercomparison Project (CMIP5) studied in Part I. It is shown that both the net radiative fluxes at TOA and the global surface temperature transient response are well represented by the simple EBM over the available period of simulations. Differences between this two-layer EBM and the previous version without an efficacy factor are analyzed and relationships between parameters are discussed. The simple model calibration applied to AOGCMs constitutes a new method for estimating their respective equilibrium climate sensitivity and adjusted radiative forcing amplitude from short-term step-forcing simulations and more generally a method to compute their global thermal properties.